FieldsIB Physics HL: Topic test

20 questions, 54 marks

IB Physics HL

Fields topic test

Total 54 marks

Name

Class

Date

1
A small moon of a gas giant planet has a radius of 1.6 × 10⁶ m and a mass of 4.8 × 10²² kg. Take G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
What is the gravitational field strength at the surface of the moon?
[1 mark]
A1.25 m s⁻²
B0.31 m s⁻²
C12.5 m s⁻²
D0.125 m s⁻²
(b)
What is the escape speed from the surface of the moon?
[1 mark]
A1.4 × 10³ m s⁻¹
B2.0 × 10³ m s⁻¹
C1.0 × 10³ m s⁻¹
D4.0 × 10⁶ m s⁻¹
(c)
A small rock is launched vertically from the surface of the moon at 1800 m s⁻¹. State, with a reason, whether it will escape the moon's gravity or fall back to the surface.
[2 marks]
Total for question 1: 4 marks
2
In an inkjet printer, a charged ink droplet of charge −1.6 × 10⁻¹³ C passes between two parallel deflecting plates 12 mm apart, across which a potential difference of 900 V is maintained.
(a)
What is the magnitude of the electric field strength between the plates?
[1 mark]
A10.8 V m⁻¹
B6.25 × 10⁶ V m⁻¹
C7.5 × 10⁴ V m⁻¹
D1.33 × 10⁻⁵ V m⁻¹
(b)
Which statement correctly describes the electric field between the two parallel plates?
[1 mark]
AThe field is strongest near the edges of the plates and weaker at the centre
BThe field lines converge to a single point midway between the plates
CNo electric field exists between the plates unless a droplet is present in it
DThe field is uniform, with parallel, equally spaced field lines pointing from the positive plate to the negative plate
(c)
Calculate the magnitude of the electric force on the ink droplet while it is between the plates.
[2 marks]
Total for question 2: 4 marks
3
A beam of ions, each of charge +2e, passes undeflected in a straight line through a region containing a uniform electric field of magnitude 2.4 × 10⁴ V m⁻¹, directed vertically downward, and a uniform magnetic field of magnitude 0.15 T, directed horizontally and perpendicular to both the ion beam and the electric field.
(a)
Explain why the ions travel undeflected through this region, and use this condition to calculate the speed of the ions.
[3 marks]
(b)
The magnetic field is now switched off, leaving only the electric field. Each ion has mass 6.64 × 10⁻²⁷ kg and charge +2e = 3.2 × 10⁻¹⁹ C. Calculate the acceleration of an ion due to the electric field alone, and describe the resulting path of the ion beam as it continues through the field region.
[4 marks]
Total for question 3: 7 marks
4
A straight conducting rod of length 0.80 m lies across a pair of horizontal, frictionless conducting rails, perpendicular to a uniform magnetic field of flux density 0.45 T that points vertically through the plane of the rails. The rails are connected by a fixed resistor of resistance 6.0 Ω, and the rest of the circuit has negligible resistance. The rod is pulled along the rails at a constant speed of 3.5 m s⁻¹.
(a)
Explain, using Faraday's and Lenz's laws, why an emf is induced in the circuit as the rod moves, calculate the magnitude of this emf, and calculate the current in the circuit.
[6 marks]
(b)
Calculate the magnetic force needed to keep the rod moving at this constant speed and the mechanical power required to do so. Show that this mechanical power equals the electrical power dissipated in the resistor, and explain the physical significance of this result in terms of conservation of energy.
[6 marks]
Total for question 4: 12 marks
5
A newly discovered exomoon orbits a giant exoplanet in a circular orbit of radius 4.2 × 10⁸ m, with an orbital period of 3.2 days. Take G = 6.67 × 10⁻¹¹ N m² kg⁻².
(a)
What is the orbital period of the exomoon expressed in seconds?
[1 mark]
A2.76 × 10⁵ s
B4.61 × 10³ s
C1.15 × 10⁴ s
D3.2 s
(b)
Which relationship, in the form of Kepler's third law, applies to this circular orbit?
[1 mark]
AT ∝ r²
BT² ∝ r³
CT² ∝ r
DT ∝ r³
(c)
Use Kepler's third law to calculate the mass of the exoplanet.
[2 marks]
Total for question 5: 4 marks
6
Two small charged spheres, P (+5.0 nC) and Q (−3.0 nC), are fixed 0.40 m apart in air. M is the midpoint of the line joining P and Q. Take k = 8.99 × 10⁹ N m² C⁻².
(a)
What is the magnitude of the electric force between P and Q?
[1 mark]
A3.4 × 10⁻⁶ N
B2.1 × 10⁻⁶ N
C8.4 × 10⁻⁷ N
D3.4 × 10⁻⁷ N
(b)
Is the force between P and Q attractive or repulsive, and why?
[1 mark]
ARepulsive, because the charges are of opposite sign
BAttractive, because the charges are of the same sign
CThere is no electric force, because the net charge of the pair is positive
DAttractive, because the charges are of opposite sign
(c)
Calculate the magnitude of the total electric field at the midpoint M, stating its direction.
[2 marks]
Total for question 6: 4 marks
7
An electron moves in a vacuum at a speed of 4.0 × 10⁶ m s⁻¹, perpendicular to a uniform magnetic field of flux density 2.5 × 10⁻³ T, and follows a circular path. Take the electron mass as 9.11 × 10⁻³¹ kg and its charge magnitude as 1.60 × 10⁻¹⁹ C.
(a)
Calculate the radius of the electron's circular path.
[3 marks]
(b)
Calculate the period of the electron's circular motion, and explain why this period does not depend on the electron's speed.
[4 marks]
Total for question 7: 7 marks
8
A planet has mass 6.4 × 10²³ kg and radius 3.4 × 10⁶ m. Consider a point at a distance of 1.0 × 10⁷ m from the centre of this planet. For comparison, consider also an isolated point charge Q = +5.0 nC in a vacuum, and a second point at a distance of 0.20 m from this charge. Take G = 6.67 × 10⁻¹¹ N m² kg⁻² and k = 8.99 × 10⁹ N m² C⁻².
(a)
For the point in the planet's gravitational field, calculate the gravitational field strength, the gravitational potential, and the escape speed from this point.
[6 marks]
(b)
For the point near the isolated point charge Q, calculate the electric field strength and the electric potential, and hence the work done in bringing a charge of +2.0 μC from infinity to this point. By comparing the equations used in (a) and (b), explain one key similarity and one key difference between gravitational and electric fields, with reference to the sign of the potential in each case.
[6 marks]
Total for question 8: 12 marks

End of questions